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Theorems · Theorem · complex analysis

AnalyticOn.cpow

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f g : E → ℂ} {s : Set E},
  AnalyticOn ℂ f s → AnalyticOn ℂ g s → (∀ z ∈ s, f z ∈ Complex.slitPlane) → AnalyticOn ℂ (fun z => f z ^ g z) s

f z ^ g z is analytic if f z avoids nonpositive reals

Defined in
Mathlib.Analysis.SpecialFunctions.Complex.Analytic
Cited by
1 results in Mathlib
Foundations
Depth 291 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpace
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Complex.one_add_cpow_hasFPowerSeriesOnBall_zero · cited by 3Complex.one_add_cpow_hasF…Set · cited by 53352SetNormedAddCommGroup · cited by 15752NormedAddCommGroupNormedSpace · cited by 12499NormedSpaceComplex · cited by 5565ComplexAnalyticOn · cited by 161AnalyticOnComplex.slitPlane · cited by 113Complex.slitPlaneAnalyticWithinAt.cpow · cited by 2AnalyticWithinAt.cpowAnalyticOn.cpowCITED BYCITES

Cites7

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Cited by1

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